Nervous Tories huddled in corners at the party's conference venue in Birmingham today wondering whether George Osborne has presided over the government's first major mistake.

"Well, my wife will certainly be voting Labour now," one senior figure said after the chancellor's announcement yesterday that child benefit will be withdrawn from higher-rate taxpayers.

Osborne alarmed Tories at all levels of the party when he announced on breakfast television early on Monday morning that child benefit would be cut from any parent earning more than £43,875. The chancellor unveiled the cut, to be introduced in 2013, a few hours before his conference speech, to lessen the shock among Tory delegates who would fear that such a move will hit their core supporters.

Osborne hoped that his audience would be cheered by what was described as a "crowd-pleasing" second announcement. This was to toughen rules for households dependent on out-of-work benefit payments by capping these to the median earned income.

But attention focused on the child benefit cuts amid fears that it would hit key Tory supporters. Osborne moved to reassure anxious Tory MPs today by emailing a letter explaining the move. The chancellor acknowledged the MPs' concerns but defended his decision on the grounds that it will raise £1bn and show that higher earners will contribute to cutting the deficit.

Osborne wrote: "In order to sustain public support for the difficult choices ahead, I believe that we must show people that our approach is not only tough but is also fair. That means showing that those at the higher end of the income scale are also affected by the measures we take."

Senior government sources indicated they might soften the blow for higher-rate taxpayers by extending a planned marriage tax allowance up the income scale.

Many Tories are concerned by what is described as the "off-the-cliff" element of changing child benefit through the tax system. Parents will lose thousands if they earn one penny over £43,875. This could mean that a single parent earning £44,000 would lose child benefit while a couple whose joint income falls below £87,750 would keep it.

David Davis said: "I am entirely in favour of restricting child benefit from the very well-off. But the actual practice that is being proposed is unwise."

It is understood the chancellor is examining whether a transferable tax allowance, due to be introduced for married couples paying the basic rate by 2015, could be extended to higher-rate taxpayers. Tory sources said the coalition agreement, which allowed the Liberal Democrats to abstain in any vote on the issue, did not specify whether this would be limited to any particular income group.

"The door is not completely slammed in the face of this," one source said of the possibility of extending the tax break.

The signals from the leadership came after loyal Tories expressed unease about the cut. Eleanor Laing, a former shadow minister, said: "I will lose child benefit and that is absolutely right. But I am concerned about the anomalies and the effects on stay-at-home mothers whose husbands earn around £44,000. But I am sure that the chancellor has plenty of time before the policy is implemented to make sure people who would lose out in this way will be compensated."

Ministers voiced fears that Osborne, regarded as the Tories' best strategist, may have been caught out by the need to act quickly before his spending review on 20 October. Iain Duncan Smith, the work and pensions secretary, said last night that the chancellor had been bounced into the move by the media.

"You were all spending your time just dwelling on this the whole time," he told an Observer fringe. "The reality is there was a sort of interest and that was why it was done."

One senior figure said: "This announcement on child benefit does bear the hallmarks of improvisation. It looks like it was done quickly to fund the welfare reforms George Osborne has agreed with Iain Duncan Smith." It appears that George did not fully think through people on the edge who will lose out badly. I am surprised because George always thinks through all their stages."